These are the raw measured values. The rows (1-9) are the different
tomography rotations (indicated after the % on each line). The column
values (1-4) are the |00>, |01>, |10> and |11> probabilities,
respectively.

p(1,2:4)=[0.32 0.36 0.08]; p(1,1)=1-sum(pops1(1,2:4)); %II
p(2,2:4)=[0.19 0.25 0.26]; p(2,1)=1-sum(pops1(2,2:4)); %XI
p(3,2:4)=[0.23 0.27 0.20]; p(3,1)=1-sum(pops1(3,2:4)); %YI
p(4,2:4)=[0.29 0.23 0.20]; p(4,1)=1-sum(pops1(4,2:4)); %IX
p(5,2:4)=[0.22 0.20 0.28]; p(5,1)=1-sum(pops1(5,2:4)); %XX
p(6,2:4)=[0.32 0.37 0.14]; p(6,1)=1-sum(pops1(6,2:4)); %YX
p(7,2:4)=[0.24 0.18 0.24]; p(7,1)=1-sum(pops1(7,2:4)); %IY
p(8,2:4)=[0.14 0.10 0.38]; p(8,1)=1-sum(pops1(8,2:4)); %XY
p(9,2:4)=[0.25 0.19 0.26]; p(9,1)=1-sum(pops1(9,2:4)); %YY

The data was then analyzed by the standard procedure of state tomography,
which involved a least square fit to get the resulting density matrix
(with and without first correcting for single qubit measurement errors, as
described in the paper). The code first reshapes the above p matrix to a
vector, and then "backslash divides" from the transformation matrix, to
find the density matrix in column form. It is then reshaped and the final
density matrix is obtained by representing the result in the
(00,01,10,11)X(00,01,10,11) basis.

The resulting density matrices are:

R1 is uncorrected for the single qubit measurement fidelity and R2 is the
corrected matrix (as described in the Science paper):

R1 =

 0.2317            -0.0383 + 0.0017i  -0.0117 - 0.0350i  -0.0100 + 0.0350i
-0.0383 - 0.0017i   0.3383             0.0700 + 0.2250i  -0.0117 + 0.0250i
-0.0117 + 0.0350i   0.0700 - 0.2250i   0.3417             0.0417 - 0.0183i
-0.0100 - 0.0350i  -0.0117 - 0.0250i   0.0417 + 0.0183i   0.0883


R2=

   0.1279          -0.0253 + 0.0388i   0.0206 - 0.0227i  -0.0172 + 0.0602i
  -0.0253-0.0388i   0.3971             0.1125 + 0.3539i   0.0128 + 0.0727i
   0.0206+0.0227i   0.1125 - 0.3539i   0.4013             0.0919 + 0.0029i
  -0.0172-0.0602i   0.0128 - 0.0727i   0.0919 - 0.0029i   0.0737